First, as Sarah told you, ensure that you have configured Duke nukem 3D to use the AWE32, instead of the FM/OPL audio or any other setting.

Then, be aware that the AWE32 emulation is not perfect.
I have been improving it for the release v13 specially in regards to its envelopes and LFOs, as well as initialization, but the filter emulation is not exact, and more importantly, the chorus and reverb emulation is in some initial stages (tries to sound like it, but it doesn't).

With that said, you should still have some satisfactory experience, compared to how FM would sound.

After trying it, I believe the problem is that you run Duke Nukem from Windows. I could reproduce your bad sound running it from inside Windows.
Boot up to DOS and it will work fine.

The reason why this could matter is that the EMU8000 (the music chip in the AWE32) needs to be controlled directly by the application using it.
Under Windows, the soundcard driver operates it in order to be able to play MIDI, but when another application wants to use it directly, it can receive conflicting instructions from two sources (Windows and the DOS application).
Other Windows applications usually talk to the windows driver with an API that they added.

Ok, after serveral executions, it seems that it is more a problem of incorrect initialization, and sometimes it just plays incorrectly.
There was a similar issues with Doom too, that was solved during development.

p.s. Sound Blaster AWE32 is the best sound card available in PCEM currently, right?

By best in ISA, having EMU8K features (some games do want them) while also having the choice to use OPL3 then yes, but there's also the SBPCI emulated which can do EAX and A3D while having very little for guaranteed dos compatibility and midi, while still being a very nice soundcard for later Windows 9X games.